Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations
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Nahmod-2013-ALMOST SURE EXISTENC.pdf
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Author(s)
Nahmod, Andrea
Pavlović, Nataša
Staffilani, Gigliola
Date Issued
January 2013
Journal
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Nahmod, Andrea R., Nataša Pavlović, and Gigliola Staffilani. “Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations.” SIAM J. Math. Anal. 45, no. 6 (January 2013): 3431–3452.
Version
Final published version
Abstract
In this paper we show that after suitable data randomization there exists a large set of supercritical periodic initial data, in $H^{-\alpha}(\boldsymbol{T}^d)$ for some $\alpha(d) > 0$, for both two- and three-dimensional Navier--Stokes equations for which global energy bounds hold. As a consequence, we obtain almost sure large data supercritical global weak solutions. We also show that in two dimensions these global weak solutions are unique.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/120882184
